Create Equations and Inequalities to Solve Problems-Algebra1-Solved Examples

Solved Examples and Worksheet for Create Equations and Inequalities to Solve Problems

Q1It cost 3 cents to copy a page. William has only $1.23 to spend on copying. Express the number of pages he can copy as an inequality.

A. x ≥ 41
B. x > 41
C. x ≤ 41
D. x < 41

Solutions

Step: 1

$1.23 = 123 cents.

[Converting dollars to cents]

Step: 2

Let x be the number of pages he can copy.

Step: 3

3x ≤ 123

[Original inequality.]

Step: 4

3x3 ≤ 1233

[Divide each side by 3.]

Step: 5

x ≤ 41

[Simplify.]

Correct Answer is : x ≤ 41

Q2George went shopping and spent $274. By the time he came back to his house, he had at least $84 in his pocket. How much did he have before he went shopping?

A. At least $358
B. $358
C. At most $442
D. None

Solutions

Step: 1

Let m be the amount George had in his pocket before he went shopping.

Step: 2

Money in George's pocket before shopping - Money spent ≥ Money left over

Step: 3

m - 274 ≥ 84

[Original inequality.]

Step: 4

m - 274 + 274 ≥ 84 + 274

[Add 274 to each side.]

Step: 5

m ≥ 358

[Simplify.]

Step: 6

George had at least $358 before he went shopping.

Correct Answer is : At least $358

Q3Katie has $186, with which she can buy at most 3 dresses. Find the maximum cost of each dress she can buy.

A. $63
B. $62
C. $61
D. None of the above

Solutions

Step: 1

Let x be the cost of each dress.

Step: 2

As she can buy at most 3 dresses, the total cost of the 3 dresses is less than or equal to $186.

Step: 3

3x ≤ 186

[Write the inequality.]

Step: 4

3x3 ≤ 1863

[Divide by 3 on each side.]

Step: 5

x ≤ 62

[Simplify.]

Step: 6

The maximum cost of each dress is $62.

[As x ≤ 62, the maximum value of x is 62.]

Correct Answer is : $62

Q4How old is Nathan now, if he will be above 15 after 6 years?
A. 9 years
B. Above 9 years
C. Below 9 years
D. None of the above

Solutions

Step: 1

Let a be the present age of Nathan.

Step: 2

a + 6 > 15

[Write an inequality.]

Step: 3

a + 6 - 6 > 15 - 6

[Subtract 6 from each side.]

Step: 4

a > 9

[Simplify.]

Step: 5

Nathan's present age is above 9 years.

Correct Answer is : Above 9 years

Q5The sum of two numbers is more than 292. If one of the numbers is 181, then which of the following numbers can be the other number?

A. 110
B. 117
C. 108
D. 109

Solutions

Step: 1

The sum of two numbers is more than 292.

[In words.]

Step: 2

Let x be the unknown number.

Step: 3

x + 181 > 292

[Original Inequality.]

Step: 4

x + 181 - 181 > 292 - 181

[Subtract 181 from each side.]

Step: 5

x > 111

[Simplify.]

Step: 6

The other number is greater than 111.

Step: 7

Among the choices, the number greater than 111 is 117.

Step: 8

So, 117 is the other number.

Correct Answer is : 117

Q6Rose wants to buy 9 burgers for her friends. She cannot spend more than $90. Find the maximum cost of each burger if she buys 9 burgers.
A. $11.32
B. $11
C. $9
D. $10

Solutions

Step: 1

Let x be the cost of each burger.

Step: 2

9x ≤ 90

[Original inequality.]

Step: 3

9x9 ≤ 909

[Divide by 9 on each side.]

Step: 4

x ≤ 10

[Simplify.]

Step: 5

The maximum cost of each burger is $10.

Correct Answer is : $10

Q7To qualify in an examination, a candidate has to get a total of 150 in two tests. Victor appeared for the exam and scored 80 in the first test. If he was qualified for the exam, then how much did he score in the second test?
A. 50
B. 60
C. 65
D. 70

Solutions

Step: 1

The total score in the two tests should at least be 150.

Step: 2

Let m be the score obtained by Victor in the second test.

Step: 3

80 + m ≥ 150

[Original inequality.]

Step: 4

80 + m - 80 ≥ 150 - 80

[Subtract 80 from each side.]

Step: 5

m ≥ 70

[Simplify.]

Step: 6

Among the choices, the value which satisfies the inequality is 70.

Step: 7

So, Victor scored 70 in the second test.

Correct Answer is : 70

Q8Edward wants to withdraw $1382.75 from his savings bank account. The minimum balance to be in any savings account is $500. What is the amount that should be there in Edward's account?
A. $1858.51
B. $1882.75
C. $1870.50
D. $1828.51

Solutions

Step: 1

Let a be the amount in Edward's savings account.

Step: 2

a - 1382.75 ≥ 500

[Write an inequality.]

Step: 3

a - 1382.75 + 1382.75 ≥ 500 + 1382.75

[Add 1382.75 to each side.]

Step: 4

a ≥ 1882.75

[Simplify.]

Step: 5

Edward should have atleast $1882.75 in his account.

Correct Answer is : $1882.75

Q9The Lake City club charges $5 per ticket for playing the lotto game. The club borrowed $1,500 from its members to organize the game. After paying back the members, the club has $1,000. How many tickets were sold for the game?

A. 400
B. 600
C. 300
D. 500

Solutions

Step: 1

Let x be the number of tickets sold.

Step: 2

5x - 1500 = 1000

[Write an equation.]

Step: 3

5x - 1500 + 1500 = 1000 + 1500

[Add 1500 on each side.]

Step: 4

5x = 2500

[Simplify.]

Step: 5

5x5 = 25005

[Divide each side by 5.]

Step: 6

x = 500

[Simplify.]

Step: 7

500 tickets were sold for the lotto game.

Correct Answer is : 500

Q10Dennis has $6 less than Tim. How much does Dennis have, if they have $14 altogether?

A. $10
B. $20
C. $4
D. $12

Solutions

Step: 1

Let x be the amount owned by Tim.

Step: 2

Amount owned by Dennis = $(x - 6)

Step: 3

x + (x - 6) = 14

[Write an equation.]

Step: 4

2x - 6 = 14

[Simplify.]

Step: 5

2x - 6 + 6 = 14 + 6

[Add 6 on each side.]

Step: 6

2x = 20

[Simplify.]

Step: 7

2x2 = 202

[Divide both sides by 2.]

Step: 8

x = 10

[Simplify.]

Step: 9

The amount owned by Tim is $10.

Step: 10

The amount owned by Dennis is $4.

[10 - 6 = 4.]

Correct Answer is : $4

Q11Ursula has $36 with her. She rents a CD player for $15 and pays a rent of $3 per day for a CD. How many CDs can she rent if she only keeps the CD(s) for one day?
A. 24
B. 7
C. 17
D. 54

Solutions

Step: 1

Let c be the number of CDs that Ursula can rent with her money.

Step: 2

36 = 15 + 3c

[Write an equation.]

Step: 3

36 - 15 = 15 + 3c - 15

[Subtract 15 from each side.]

Step: 4

21 = 3c

[Combine like terms.]

Step: 5

213 = 3c3

[Divide each side by 3.]

Step: 6

7 = c

[Simplify.]

Step: 7

Ursula can rent 7 CDs.

Correct Answer is : 7

Q12William had $28 in his wallet. He bought a burger for $16 and bought pastries with the remaining amount. Each pastry was priced at $4. How many pastries did William buy?
A. 5
B. 2
C. 3
D. 4

Solutions

Step: 1

Let p be the number of pastries that William bought.

Step: 2

28 = 16 + 4p

[Write an equation.]

Step: 3

28 - 16 = 16 + 4p - 16

[Subtract 16 from each side.]

Step: 4

12 = 4p

[Combine like terms.]

Step: 5

124 = 4p4

[Divide each side by 4.]

Step: 6

3 = p

[Simplify.]

Step: 7

William bought 3 pastries.

Correct Answer is : 3

Q13Mike paid $2.65 for 3 pencils and 1 eraser. Find the cost of one pencil, if the cost of eraser is $0.40

A. $0.75
B. $1.15
C. $0.35
D. $2.15

Solutions

Step: 1

Let c be the cost of one pencil.

Step: 2

3 pencils cost + 1 eraser cost = 2.65

Step: 3

3c + 0.40 = 2.65

[Write the equation.]

Step: 4

3c + 0.40 - 0.40 = 2.65 - 0.40

[Subtract 0.40 from each side.]

Step: 5

3c = 2.25

[Simplify.]

Step: 6

3c3 = 2.253

[Divide each side by 3.]

Step: 7

c = 0.75

[Simplify.]

Step: 8

The cost of one pencil is $0.75

Correct Answer is : $0.75

Q14Find the value of t, if the perimeter of the triangle is 19 cm.

A. 4
B. 5
C. 6
D. 3

Solutions

Step: 1

The perimeter of a triangle is equal to the sum of its sides.

Step: 2

19 = (t + 2) + (t + 4) + (2t - 3)

[Substitute the values.]

Step: 3

19 = 4t + 3

[Combine like terms.]

Step: 4

19 - 3 = 4t + 3 - 3

[Subtract 3 from each side.]

Step: 5

16 = 4t

[Simplify.]

Step: 6

164 = 4t4

[Divide each side by 4.]

Step: 7

4 = t

[Simplify.]

Step: 8

The value of t is 4 .

Correct Answer is : 4

Q15Jake has $4 less than John. How much does Jake have, if they have $18 altogether?
A. $22
B. $16
C. $7
D. $11

Solutions

Step: 1

Let $x be the amount owned by John.

Step: 2

Amount owned by Jake = $(x - 4)

Step: 3

x + (x - 4) = 18

[Write an equation.]

Step: 4

2x - 4 = 18

[Simplify.]

Step: 5

2x - 4 + 4 = 18 + 4

[Add 4 on each side.]

Step: 6

2x = 22

[Simplify.]

Step: 7

2x2 = 222

[Divide both sides by 2.]

Step: 8

x = 11

[Simplify.]

Step: 9

The amount owned by John is $11.

Step: 10

The amount owned by Jake is $7.

[11 - 4 = 7.]

Correct Answer is : $7

Solved Examples and Worksheet for Create Equations and Inequalities to Solve Problems

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